Problem: Solve for $x$ : $10\sqrt{x} - 9 = 5\sqrt{x} + 10$
Subtract $5\sqrt{x}$ from both sides: $(10\sqrt{x} - 9) - 5\sqrt{x} = (5\sqrt{x} + 10) - 5\sqrt{x}$ $5\sqrt{x} - 9 = 10$ Add $9$ to both sides: $(5\sqrt{x} - 9) + 9 = 10 + 9$ $5\sqrt{x} = 19$ Divide both sides by $5$ $\frac{5\sqrt{x}}{5} = \frac{19}{5}$ Simplify. $\sqrt{x} = \dfrac{19}{5}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{19}{5} \cdot \dfrac{19}{5}$ $x = \dfrac{361}{25}$